Linear Functional Equations and Twisted Polynomials

A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.

Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

Some Modified Equations of the Sine-Hilbert Type

Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.

Enhancing Proficiency in Quadratic Equations and Functions Through the MILAPlus Strategy

This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School.

Functional near-infrared spectroscopy in non-invasive neuromodulation

Non-invasive cerebral neuromodulation technologies are essential for the reorganization of cerebral neural networks,which have been widely applied in the field of central neurological diseases,such as stroke,Parkinson’s disease,and mental disorders.Although significant advances have been made in neuromodulation technologies,the identification of optimal neurostimulation paramete rs including the co rtical target,duration,and inhibition or excitation pattern is still limited due to the lack of guidance for neural circuits.Moreove r,the neural mechanism unde rlying neuromodulation for improved behavioral performance remains poorly understood.Recently,advancements in neuroimaging have provided insight into neuromodulation techniques.Functional near-infrared spectroscopy,as a novel non-invasive optical brain imaging method,can detect brain activity by measuring cerebral hemodynamics with the advantages of portability,high motion tole rance,and anti-electromagnetic interference.Coupling functional near-infra red spectroscopy with neuromodulation technologies offe rs an opportunity to monitor the cortical response,provide realtime feedbac k,and establish a closed-loop strategy integrating evaluation,feedbac k,and intervention for neurostimulation,which provides a theoretical basis for development of individualized precise neuro rehabilitation.We aimed to summarize the advantages of functional near-infra red spectroscopy and provide an ove rview of the current research on functional near-infrared spectroscopy in transcranial magnetic stimulation,transcranial electrical stimulation,neurofeedback,and braincomputer interfaces.Furthermore,the future perspectives and directions for the application of functional near-infrared spectroscopy in neuromodulation are summarized.In conclusion,functional near-infrared spectroscopy combined with neuromodulation may promote the optimization of central pellral reorganization to achieve better functional recovery form central nervous system diseases.

Beyond functional MRI signals:molecular and cellular modifiers of the functional connectome and cognition

Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.This resting activity can be assessed with several in vivo tools,such as resting-state functional magnetic resonance imaging.This technique measures subtle changes in blood flow,volume,and oxygenation that occur over time.Although vascular in nature,resting-state functional magnetic resonance imaging is considered a reliable proxy of neural activity and several studies have shown that the brain is functionally divided into interacting neural networks called the“functional connectome”.

A divergent pattern in functional connectivity: a transdiagnostic perspective

Functional magnetic resonance imaging(fMRI)is a popular tool used to investigate not only how the brain responds to specific stimuli during sensorimotor or cognitive tasks,but also brain activity at rest.The physics beyond this approach is based on the analysis of the blood oxygenation level-dependent signal.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Advances in functional MRI research in bipolar disorder:from the perspective of mood states

Bipolar disorder is characterised by recurrent and alternating episodes of mania/hypomania and depression.Current breakthroughs in functional MRI techniques have uncovered the functional neuroanatomy of bipolar disorder.However,the pathophysiology underlying mood instability,mood switching and the development of extreme mood states is less well understood.This reviewpresents a comprehensive overviewof current evidence from functional MRI studies from the perspective of mood states.We first summarise the disrupted brain activation patterns and functional connectivity that have been reported in bipolar disorder,irrespective of the mood state.We next focus on research that solely included patients in a single mood state for a better understanding of the pathophysiology of bipolar disorder and research comparing patients with different mood states to dissect mood state-related effects.Finally,we briefly summarise current theoretical models and conclude this review by proposing potential avenues for future research.A comprehensive understanding of the pathophysiology with consideration of mood states could not only deepen our understanding of how acute mood episodes develop at a neurophysiological level but could also facilitate the identification of biological targets for personalised treatment and the development of new interventions for bipolar disorder.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Functional Capacity of Patients with Venous Thromboembolic Disease Six to Twelve Months after Treatment

Background: Venous thromboembolism (VTE) is among the leading causes of hospital-related disability-adjusted life years lost. We aimed to determine the prevalence and determinants of functional capacity impairment six to twelve months after an acute VTE event. Methods: This was a cross-sectional study conducted between January and April 2021 in two referral hospitals of Yaoundé, including consenting adult patients admitted to these hospitals six to twelve months ago for VTE. We excluded dead patients and those with any comorbidity or symptoms limiting physical activity. The functional outcome was assessed with the six-minute walk test. Functional capacity impairment was defined as walking distance lower than the expected value. Results: We included 27 cases in this study with a mean age of 53.2 ± 14.4 years. The prevalence of functional capacity impairment was 29.6% (95% CI: 14.8 - 48.1). Factors associated with poor functional outcome were obesity (OR: 59.5;95% CI: 4.6 - 767.2;p - 207.4;p = 0.017), massive PE (OR: 30;95% CI: 2.5 - 354;p = 0.004), and poor adherence to treatment (OR: 30.3;95% CI: 2.5 - 333.3;p = 0.004). Conclusion: Functional capacity impairment is common in the medium-term after VTE and factors associated with this poor outcome are obesity, the severity of the VTE, and poor adherence to treatment.

On entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

Dietary supplementation of zinc oxide modulates intestinal functionality during the post-weaning period in clinically healthy piglets

Background To improve our understanding of host and intestinal microbiome interaction,this research investigated the effects of a high-level zinc oxide in the diet as model intervention on the intestinal microbiome and small intestinal functionality in clinically healthy post-weaning piglets.In study 1,piglets received either a high concentration of zinc(Zn)as zinc oxide(Zn O,Zn,2,690 mg/kg)or a low Zn concentration(100 mg/kg)in the diet during the post weaning period(d 14–23).The effects on the piglet's small intestinal microbiome and functionality of intestinal tissue were investigated.In study 2,the impact of timing of the dietary zinc intervention was investigated,i.e.,between d 0–14 and/or d 14–23 post weaning,and the consecutive effects on the piglet's intestinal functionality,here referring to microbiota composition and diversity and gene expression profiles.Results Differences in the small intestinal functionality were observed during the post weaning period between piglets receiving a diet with a low or high concentration Zn O content.A shift in the microbiota composition in the small intestine was observed that could be characterized as a non-pathological change,where mainly the commensals inter-changed.In the immediate post weaning period,i.e.,d 0–14,the highest number of differentially expressed genes(DEGs)in intestinal tissue were observed between animals receiving a diet with a low or high concentration Zn O content,i.e.,23 DEGs in jejunal tissue and 11 DEGs in ileal tissue.These genes are involved in biological processes related to immunity and inflammatory responses.For example,genes CD59 and REG3G were downregulated in the animals receiving a diet with a high concentration Zn O content compared to low Zn O content in both jejunum and ileum tissue.In the second study,a similar result was obtained regarding the expression of genes in intestinal tissue related to immune pathways when comparing piglets receiving a diet with a high concentration Zn O content compared to low Zn O content.Conclusions Supplementing a diet with a pharmaceutical level of Zn as Zn O for clinically healthy post weaning piglets influences various aspects intestinal functionality,in particular in the first two weeks post-weaning.The model intervention increased both the alpha diversity of the intestinal microbiome and the expression of a limited number of genes linked to the local immune system in intestinal tissue.The effects do not seem related to a direct antimicrobial effect of Zn O.

Structural and functional connectivity of the whole brain and subnetworks in individuals with mild traumatic brain injury:predictors of patient prognosis

Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

Density functional theory study of B- and Si-doped carbons and their adsorption interactions with sulfur compounds

Understanding the adsorption interactions between carbon materials and sulfur compounds has far-reaching impacts,in addition to their well-known important role in energy storage and conversion,such as lithium-ion batteries.In this paper,properties of intrinsic B or Si single-atom doped,and B-Si codoped graphene(GR)and graphdiyne(GDY)were investigated by using density functional theory-based calculations,in which the optimal doping configurations were explored for potential applications in adsorbing sulfur compounds.Results showed that both B or Si single-atom doping and B-Si codoping could substantially enhance the electron transport properties of GR and GDY,improving their surface activity.Notably,B and Si atoms displayed synergistic effects for the codoped configurations,where B-Si codoped GR/GDY exhibited much better performance in the adsorption of sulfurcontaining chemicals than single-atom doped systems.In addition,results demonstrated that,after B-Si codoping,the adsorption energy and charge transfer amounts of GDY with sulfur compounds were much larger than those of GR,indicating that B-Si codoped GDY might be a favorable material for more effectively interacting with sulfur reagents.

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations

The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.